Common Core Math

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Many people have strong opinions about what is commonly known as Common Core Math. As with most things, the general, popular opinion of laypersons is usually wrong.

This has a number of parallels to small arms instruction. Personnel with minimal experience (which describes most military and law enforcement) assume their limited exposure is The Way and anything that deviates from that must be wrong because they’ve never bothered to consider it.

It’s also similar to anti-gun arguments. Non-shooters with little-to-no formal firearm education that know little-to-nothing about guns and unwilling to study the matter beyond looking at memes are only too happy to spew their opinions on it and demand their way into public policy. Similarly, non-mathematicians with little-to-no formal math education that know little-to-nothing about what the common core approach is intended to teach and unwilling to study the matter beyond looking at memes are only too happy to spew their opinions on it and demand their way into public policy.

As a non-mathematician, my initial, layperson, knee-jerk reaction was similar to the common, negative response: “What is this? That’s not how I learned it!” Then, I took the path less traveled. Within minutes, I was able to Google up writings and videos from the mathematicians that created it (including the video by Dr. Jo Boaler below) and quickly reversed my opinion. Part of the approach is learning how to learn. I quickly found similarities with this teaching approach to what is needed to understand theories in computer science. A few examples:

https://www.ece.ucsb.edu/~parhami/pubs_folder/parh02-arith-encycl-infosys.pdf

https://plato.stanford.edu/entries/lambda-calculus/
https://en.wikipedia.org/wiki/Lambda_calculus

https://en.wikipedia.org/wiki/Relational_algebra

https://en.wikipedia.org/wiki/Big_O_notation

For a given program’s computation, a programmer may not need math knowledge beyond simple arithmetic, however, that doesn’t teach the theory behind how a computer works. Understanding the how and why behind the scenes requires a level of knowledge beyond working a simple algorithm.

Doing math “like they used to teach it” is mechanically working a single, basic algorithm without really understanding. Showing how to solve the same program in different ways “backwards and forwards, inside and out” demonstrates a full command of the knowledge. It’s not about which way is faster (use a spreadsheet or MATLAB if you want the answer fast), it’s about a more deep understanding.

Consider these explanations of the rationale of this education approach by some of the mathematicians that created it. This will take longer and require more deep thinking than blindly sharing and/or liking idiotic memes on social media. Perhaps that’s the cause of the real problem.

https://www.salon.com/2015/11/28/youre_wrong_about_common_core_math_sorry_parents_but_it_makes_more_sense_than_you_think/amp



From Michael Goldenberg The mistake here is pretending that there is any such animal as “Common Core Math.” There is not. There is a set of content standards; there is a set of standards of practice for both students and teachers (which is very similar to the Process Standards from NCTM going back more than a decade).  And then there are a bunch of curricular packages (mostly textbook series for various grade bands, but also some online material, most notably (and horridly) ENGAGE-NY, which has been forced on all public schools in NY State and Louisiana). Those materials are not “the Common Core” but merely various implementations that CLAIM to be aligned to the standards. Period. So anyone who uses the term “Common Core Math” other than to refer to the standards is in error. And that goes for Dr. Boaler, much as I respect her and her work. It’s just silly and misleading and dangerous to pretend that there is some monolithic entity that is isomorphic to COMMON CORE MATH. There isn’t. And likely won’t be. 

Those who know the history of math education in the US know about “The” New Math, c. late 1950s into the early 1970s. But again, no such animal ever existed. There were a bunch of separate projects funded by the federal government to design new approaches to math. Some produced textbooks, but few of those got published and distributed past the pilot schools/district with which each individual project worked. One series, however, did get widely published and used: the Dolciani series. Some people, including people who generally hate what NCTM was pushing in the ’90s and henceforth and also hate “Common Core Math” to the extent that it is similar to those ’90s reform math texts, really LOVE Dolciani. Others despise it. I have mixed feeling about the series. It is VERY formalistic, much more like college math books than anything that appeared in the US prior to the ’60s for K-12.

As someone who now knows a lot of math, they’re okay. But as a kid, I probably would have found them dry and off-putting. And my dad, who had to try to help my younger brothers with homework out of those books, was at a loss, despite having studied math through calculus in school. It was too far from his own experience.  What we see now is people who are reacting against Common Core math books similarly to how my father reacted in the ’60s to Dolciani, but he didn’t blame everything on Obama. He didn’t blame it on Eisenhower or JFK, either. He just knew that he was out of his depth.  

Note, I’m NOT claiming that all the materials being hawked by publishers as “Common Core Math” are any good. Maybe NONE of them are. But that’s not really the issue. Most of what people are screaming about and finding a host of conspiracies behind (see all the crazy videos and many of the nastier comments against Common Core) is just ideas about teaching math better that have been around for decades.

The math isn’t new, and neither, really, is most of the pedagogy. Most of it makes perfect sense if done intelligently, but of course is confusing if it’s presented badly (seriously, folks: what ISN’T confusing in math if presented badly?) or if you’ve never seen it before and are so angry that you won’t even stop to think about how it might be sensible either because you’re embarrassed to say to your child that you simply don’t get it.

Bottom line: calm the fudge down, folks. When the smoke clears and the Common Core is gone, most professionals in math education will still want your kids to learn how to approach math more deeply and thoughtfully than you were presented with. That’s the nature of people who actually care about more than a small elite learning math. I’m one of them. Jo Boaler is one of them. There are thousands of us out there. We’re (mostly) pretty smart folks who spend our lives studying math, kids, learning, and teaching.

You may certainly disagree with anything or everything we think and say, but that doesn’t make it communism or corporate capitalism, either. You can fight it, but you’re not really helping your kids when you do so blindly and with great prejudice, when you swallow every horror story your read and hear, when you react out of fear and ignorance (and tell yourself it’s really out of deep knowledge of mathematics and its teaching, when few Americans really know mathematics deeply or are at all familiar with research on teaching and learning the subject at various levels), and kick and scream that you know more about all this than any college professor or K-12 teacher (you might be right to some extent about any given teacher, of course).

I wait patiently for parents who take the time to actually think rather than just react emotionally. Those who do the former often find that there’s a good deal to like out there, no matter what label is put on it, and the anti-Communist lunatics who post videos here are for the most part out of their minds. But of course, if you need to believe that progressive math (before or after the Common Core label got placed on it) is really about “dumbing down” kids, be my guest. Your loss, and, sadly, your kids’ loss. 

Traits of the Very Best Leaders

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Spoiler: It’s also the opposite of every drill sergeant stereotype and other incompetent leaders in the military.

Google’s research is in line with the Disciplined Disobedience approach that the Army is supposed to be following but few personnel actually do.

1. Be a good coach.
You either care about your employees or you don’t. There’s no gray zone. If you care, then you’ll invest time and energy to help your employees become better versions of themselves. That’s the first 50 percent of being a good coach.

The other half is knowing you’re a facilitator, not a fixer. Ask good questions, don’t just give the answers. Expand your coachees’ point of view versus giving it to them.

2. Empower teams and don’t micromanage.
Absolutely no one likes to be micromanaged. Research indicates empowered employees have higher job satisfaction and organizational commitment, which reduces turnover and increases performance and motivation. Also, supervisors who empower are seen as more influential and inspiring by their subordinates.

Everyone wins when you learn to let go.

3. Create an inclusive team environment, showing concern for success and well-being.
Individual fulfillment is often a joint effort. People derive tremendous joy from being part of a winning team. The best managers facilitate esprit de corps and interdependence.

And employees respond to managers who are concerned about winning, and winning well (in a way that supports their well-being).

4. Be productive and results oriented.
Take productivity of your employees seriously and give them the tools to be productive, keeping the number of processes to a minimum.

5. Be a good communicator — listen and share information.
The biggest problem with communication is the illusion that it has taken place. It often doesn’t happen because of a lack of effort from both the transmitting and the receiving parties. Invest in communication, and care enough to listen.

Former CEO of Procter & Gamble A.G. Lafley once told me his job was 90 percent communication–communicating the next point especially.

6. Have a clear vision/strategy for the team.
With no North Star, employees sail into the rocks. Enroll employees in building that vision/strategy, don’t just foist it on them. The former nets commitment, the latter compliance. And be prepared to communicate it more often than you ever thought you could.

7. Support career development and discuss performance.
The best managers care about their people’s careers and development as much as they care about their own. People crave feedback. And you owe it to them.

People don’t work to achieve a 20 percent return on assets or any other numerical goal. They work to bring meaning into their lives, and meaning comes from personal growth and development.

8. Have the expertise to advise the team.
Google wants its managers to have key technical skills (like coding, etc.) so they can share the “been there, done that” experience. So be there and do that to build up your core expertise, whatever that might be. Stay current on industry trends and read everything you can.

9. Collaborate.
In a global and remote business world, collaboration skills are essential. Collaboration happens when each team member feels accountability and interdependence with teammates. Nothing is more destructive for a team than a leader who is unwilling to collaborate. It creates a “it’s up to only us” vibe that kills culture, productivity, and results.

10. Be a strong decision maker.
The alternative is indecision, which paralyzes an organization, creates doubt, uncertainty, lack of focus, and even resentment. Strong decisions come from a strong sense of self-confidence and belief that a decision, even if proved wrong, is better than none.

https://www.inc.com/scott-mautz/google-tried-to-prove-managers-dont-matter-instead-they-discovered-10-traits-of-very-best-ones.html

Why Has Competition Slowed?

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http://gunsmagazine.com/classic-guns-magazine-editions/
Review these old gun magazines and you’ll see the importance of competition back in the 1950 and 1960s.

http://www.gunsmagazine.com/1956issues/G1256.pdf


page 5-6, lists various match results

http://www.gunsmagazine.com/1958issues/G0258.pdf


page 5, Bill Toney, Askins, Hebard competition shooters writing articles with content about competitions
“My Favorite Gun” section features a conventional pistol competitor.

http://www.gunsmagazine.com/1956issues/G0756.pdf


page 14, “Why Doesn’t Shooting Go Professional?”
That issue began with an interview with pistol champ Harry Reeves.

http://www.gunsmagazine.com/1960issues/G0260.pdf


Four competition articles. The magazine has a specific “Competition” section because it regularly published enough material on this in every issue to warrant a dedicated section.

Consider the state of the NRA membership and its Competition Division back in 1961.

Back then, with a membership of 418,000 total, the NRA boasted 120,367 classified competitors and the Marksmanship Qualification Program had 374,112 participants. That is, roughly 29% of the membership was classified in formal competition and 90% participated in the MQP. Page 49 of that same issue details a drive for 500,000 members by using the Marksmanship Qualification Program and a push to get every NRA member involved.

Today, with over 4 million members, a tenfold increase, less than 100,000 members are classified shooters (about 2%) and the Marksmanship Qualification Program isn’t even tracked despite advances in information processing and computers.

Some time ago, I was considered for a writing job sponsored by a nationally-recognized firearm/outdoor distributor and edited by a nationally-recognized publisher with a readership of around a quarter million subscribers. The Editor-In-Chief, who knew me from my various writing and editing work as well as my competitive shooting background, told me plainly they would not entertain any formal marksmanship instruction material and specifically shunned competition-specific coverage. This wasn’t due to a bias from the company, publisher, or editor, rather, it was due to them tracking reader feedback. Detailed marksmanship training beyond introductory fluff tracked the lowest interest and anything competition specific was notably poor. The subscribers simply weren’t interested. They were rather interested in gear reviews, product releases, and gun politics. So the general gun owning public is vitally interested in being told what toys to buy and maintaining their right to continue doing so but has little interest in how to actually use the stuff beyond a novice level.

Fixing the Army’s Broken Culture

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Military elements often retain a degree of tradition, sometimes to their detriment and well past any meaningful use. Examples include the foolish and ineffective approach that initial entry training (“basic”) continues to be conducted and long-obsolete and useless holdovers such as drill and ceremony. I’ll begrudge an exception to D&C for personnel formally directed to conduct a tattoo while also pointing out the general fraud, waste, and abuse of such pompous displays.

Things like this are continued under the false guise of instilling discipline and learning how to pay attention to detail despite no evidence that they accomplish either:

http://changingminds.org/disciplines/leadership/styles/lewin_style.htm
http://www.kurt-lewin.com/leadership-styles.shtml

Kurt Lewin’s research on leadership and group dynamics indicates an over-bearing authoritative approach typified by the drill sergeant stereotype may be the worst way to lead people in many situations, especially if you want them to be capable of thinking and leading on their own one day. Test groups can revert to even worse undisciplined behavior than those put into laissez-faire control groups when the authority figure is removed. If you enforce babysitting measures upon personnel as the only means of enforcing discipline, then you’ll have to always and forever ensure a babysitter is present.

Forward-thinking leaders have commented on the need to break obsolete and detrimental traditions, even directing that future leaders must be able to function under disciplined disobedience.

Here are some examples:

https://soflete.com/blogs/knowledge/surfers-hippies-hipsters-and-snowflakes-counterculture-in-sof

https://www.army.mil/article/187293/future_warfare_requires_disciplined_disobedience_army_chief_says

Traits of the best leaders/managers (hint, it’s the opposite of the drill sergeant stereotype and what every bad “leader” does)
https://www.inc.com/scott-mautz/google-tried-to-prove-managers-dont-matter-instead-they-discovered-10-traits-of-very-best-ones.html

Future warfare requires ‘disciplined disobedience,’ Army chief says

“I think we’re over-centralized, overly bureaucratic, and overly risk-averse,” Chief of Staff of the Army Gen. Mark A. Milley said while speaking at the Army and Navy Club in Washington, D.C., as part of the Atlantic Council Commanders Series.

Leaders on the battlefield could expect to be out of contact with their own leadership for significant periods of time. Those officers would still need to accomplish their commander’s objectives, even when the conditions on the battlefield change and they are unable to send word up the chain of command.

“We are going to have to empower [and] decentralize leadership to make decisions and achieve battlefield effects in a widely dispersed environment where subordinate leaders, junior leaders … may not be able to communicate to their higher headquarters, even if they wanted to,” Milley said.

In that environment, Milley said, the Army will need a cadre of trusted leaders on the battlefield who know when it’s time to disobey the original orders they were given and come up with a new plan to achieve the purpose of those orders.

“[A] subordinate needs to understand that they have the freedom and they are empowered to disobey a specific order, a specified task, in order to accomplish the purpose. It takes a lot of judgment.”

Such disobedience cannot be “willy-nilly.” Rather, it must be “disciplined disobedience to achieve a higher purpose,” Milley said. “If you do that, then you are the guy to get the pat on the back.”

Milley said that when orders are given, the purpose of those orders must also be provided so that officers know both what they are to accomplish and how they are expected to accomplish it.

More:
https://www.army.mil/article/187293/future_warfare_requires_disciplined_disobedience_army_chief_says

None of this is new. This formal 1978 study Military Self-Discipline: A Motivational Analysis reveals the same things
http://www.dtic.mil/dtic/tr/fulltext/u2/a055017.pdf

Worst of all, despite having formal, studied, decades-old evidence that a self-discipline approach selects for and produces better outcomes than an overbearing, authoritative approach, there is NO formal evidence that the current model provides any benefit.

The topic of leadership has been extensively studied in a range of occupational settings. Findings indicate that employee ratings of leaders predict occupational outcomes such as job turnover, satisfaction, and performance in both military and civilian occupational settings.

Approximately 72,000 soldiers go through Army BCT in the United States each year (http://www.jackson.army.mil/sites/info/) … [A]lthough there are several possible leadership qualities that could be displayed by Drill Sergeants, from being harsh and demanding to mentoring and motivating, there have been NO studies that have systematically assessed Drill Sergeant characteristics. [emphasis added]

Trainee Perceptions of Drill Sergeant Qualities During Basic Combat Training was published in 2013. The Department of Army spends money to send 72,000 new recruits through initial entry “basic” training every year and has done so for many decades but has never bothered to study if the established approach is effective.

Despite the hallucinations of personnel imagining that the stereotypical drill sergeant approach is “necessary” or even useful, there is no evidence for it. Some managers have noted that running a busy restaurant may be an ideal way to develop leaders:
https://www.wsj.com/articles/if-you-can-manage-a-waffle-house-you-can-manage-anything-11572667205

What has the Army response to this been? As expected of the illiterate majority, more of the same failed nonsense.

https://www.military.com/daily-news/2018/04/24/army-making-more-drill-sergeants-increase-discipline-ait.html

https://www.armytimes.com/news/your-army/2017/11/28/its-official-the-army-is-bringing-drill-sergeants-back-to-ait/

Army Combat Fitness/Readiness Test complaints

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Here is all you need to understand about the Army’s new ACFT: Motivated and intelligent personnel that know how to train effectively will continue to get very good scores, just as before. Malingerers will complain and do poorly or fail, just as before.

Consider what the test is asking personnel to do. Here are the proposed standards as of July 31 2018: July 2018 proposed standards

The ACFT Field Testing Manual explains the standards.

https://www.military.com/sites/default/files/2018-09/Field%20testing%20manual.pdf

This article demonstrates the events:
https://www.military.com/daily-news/2018/10/30/videos-heres-how-complete-new-army-fitness-test.html
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Lies of Gurus

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What happens when a skilled competitor used to achieving measurable results in organized competition is held up against widely-accepted tactical gurus that aren’t normally tested?


Kiai Master (black karategi with red belt) offers a 5,000 dollar challenge that he can beat any MMA competitor.


MMA competitor Xu Xiaodong (black shirt and shorts) demonstrates his competition approach a "thunder style" martial arts master.

https://mobile.nytimes.com/2017/05/10/world/asia/mma-martial-arts-china-tai-chi.html?referer=android-app://m.facebook.com

Interesting, Xu Xiaodong (the MMA competitor in the second video decisively winning this challenge against the “thunder style” martial arts master) has been lambasted for his victory because it “violates the morals of martial arts.”

Based on observing and participating in the range activity of tens of thousands of military personnel and comparing that to the range activity (training and competition) of competition shooters over the decades, there are direct parallels.

What the gamer does is not real, even though he actually does it.
What the tactician does is real, even though he likely has never done it.

And should the gamer beat the tactician (who allegedly operates where there are no rules) it’s an “outrage” for “violating morals.”

Wake Up Call

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This won’t make me any friends, but I’ll say it anyway. I’ll defer to George Patton’s wisdom and have at it. More

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